Numerical Algorithms

, Volume 59, Issue 4, pp 561–569 | Cite as

A note on spectrum analysis of augmentation block Schur complement preconditioners

  • Zhi-Hao Cao
Original Paper


In this note, as a generalization of the preconditioner presented by Greif et al. (SIAM J Matrix Anal Appl 27:779–792, 2006), we consider a set of augmentation block Schur complement preconditioners for solving saddle point systems whose coefficient matrices have singular (1,1) blocks. The spectral properties of the preconditioned matrices are analyzed and an optimal preconditioner is derived.


Block preconditioners Saddle point systems Minimal polynomial Augmentation Nullity 

AMS 2000 Subject Classifications

65F10 65N20 


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Copyright information

© Springer Science+Business Media, LLC. 2011

Authors and Affiliations

  1. 1.School of Mathematical Sciences and Laboratory of Mathematics for Nonlinear SciencesFudan UniversityShanghaiPeople’s Republic of China

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